Algebraic Functions - Quadratic to Sum and Product - with Negatives (Level 1) - Mobius Math Academy

Algebraic Functions

Quadratic to Sum and Product - with Negatives (Level 1)

This math topic focuses on the relationship between the roots (a and b) of a quadratic equation and their sum and product. Each problem provides a quadratic equation in the form of \(x^2 + cx + d = (x+a)(x+b)\) and multiple choices for the values of \(a+b\) (sum of the roots) and \(ab\) (product of the roots). Students must determine which pair of values correctly corresponds to the roots of the given quadratic equation. This exercises students' understanding of polynomial algebra, specifically how the coefficients of a quadratic equation relate to the sum and product of its roots.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Algebraic Functions - Quadratic to Sum and Product - with Negatives Worksheet

Algebraic Functions - Quadratic to Sum and Product - with Negatives

What is true about 'a' and 'b' for this quadratic?

$A LaTex expression showing x to the power of 2 - 1x + -42\\=(x+a)(x+b)$

a $A LaTex expression showing a + b = -42\\a multiplied by b = -1$

b $A LaTex expression showing a + b = -2\\a multiplied by b = -42$

c $A LaTex expression showing a + b = -1\\a multiplied by b = -42$

d $A LaTex expression showing a + b = -1\\a multiplied by b = -84$

What is true about 'a' and 'b' for this quadratic?

$A LaTex expression showing x to the power of 2 + 3x + -18\\=(x+a)(x+b)$

a $A LaTex expression showing a + b = 3\\a multiplied by b = -18$

b $A LaTex expression showing a + b = 3\\a multiplied by b = -36$

c $A LaTex expression showing a + b = -18\\a multiplied by b = 3$

d $A LaTex expression showing a + b = 6\\a multiplied by b = -18$

What is true about 'a' and 'b' for this quadratic?

$A LaTex expression showing x to the power of 2 - 8x + 15\\=(x+a)(x+b)$

a $A LaTex expression showing a + b = -8\\a multiplied by b = 30$

b $A LaTex expression showing a + b = -8\\a multiplied by b = 15$

c $A LaTex expression showing a + b = -16\\a multiplied by b = 15$

d $A LaTex expression showing a + b = 15\\a multiplied by b = -8$

What is true about 'a' and 'b' for this quadratic?

$A LaTex expression showing x to the power of 2 - 6x + -27\\=(x+a)(x+b)$

a $A LaTex expression showing a + b = -6\\a multiplied by b = -54$

b $A LaTex expression showing a + b = -6\\a multiplied by b = -27$

c $A LaTex expression showing a + b = -12\\a multiplied by b = -27$

d $A LaTex expression showing a + b = -27\\a multiplied by b = -6$

What is true about 'a' and 'b' for this quadratic?

$A LaTex expression showing x to the power of 2 - 5x + 4\\=(x+a)(x+b)$

a $A LaTex expression showing a + b = -5\\a multiplied by b = 4$

b $A LaTex expression showing a + b = 4\\a multiplied by b = -5$

c $A LaTex expression showing a + b = -5\\a multiplied by b = 8$

d $A LaTex expression showing a + b = -10\\a multiplied by b = 4$

What is true about 'a' and 'b' for this quadratic?

$A LaTex expression showing x to the power of 2 - 7x + -8\\=(x+a)(x+b)$

a $A LaTex expression showing a + b = -14\\a multiplied by b = -8$

b $A LaTex expression showing a + b = -8\\a multiplied by b = -7$

c $A LaTex expression showing a + b = -7\\a multiplied by b = -8$

d $A LaTex expression showing a + b = -7\\a multiplied by b = -16$

What is true about 'a' and 'b' for this quadratic?

$A LaTex expression showing x to the power of 2 + 8x + 16\\=(x+a)(x+b)$

a $A LaTex expression showing a + b = 16\\a multiplied by b = 16$

b $A LaTex expression showing a + b = 16\\a multiplied by b = 8$

c $A LaTex expression showing a + b = 8\\a multiplied by b = 16$

d $A LaTex expression showing a + b = 8\\a multiplied by b = 32$

What is true about 'a' and 'b' for this quadratic?

$A LaTex expression showing x to the power of 2 - 10x + 9\\=(x+a)(x+b)$

a $A LaTex expression showing a + b = 9\\a multiplied by b = -10$

b $A LaTex expression showing a + b = -10\\a multiplied by b = 9$

c $A LaTex expression showing a + b = -20\\a multiplied by b = 9$

d $A LaTex expression showing a + b = -10\\a multiplied by b = 18$